Division by three
Logic
2007-05-23 v1 Combinatorics
Abstract
We prove without appeal to the Axiom of Choice that for any sets A and B, if there is a one-to-one correspondence between 3 cross A and 3 cross B then there is a one-to-one correspondence between A and B. The first such proof, due to Lindenbaum, was announced by Lindenbaum and Tarski in 1926, and subsequently `lost'; Tarski published an alternative proof in 1949. We argue that the proof presented here follows Lindenbaum's original.
Cite
@article{arxiv.math/0605779,
title = {Division by three},
author = {Peter G. Doyle and John Horton Conway},
journal= {arXiv preprint arXiv:math/0605779},
year = {2007}
}
Comments
Version dated 1994